A strikingly disproportionate number of notable theologians who influenced the American Founding and establishment of political “republicanism” were theological unitarians. These figures, British and American Whigs, were instrumental in arguing on behalf of the American Revolutionary cause and in convincing the populace that political liberty was a God-given “inalienable” right. These theologians also, in large part, shaped the personal religious creed of America’s key Founders.
None other than Mark Noll, the preeminent scholar of America’s religious history has noted “[i]t was only when Christian orthodoxy gave way that republicanism could flourish.” A characteristic feature of Founding era republicanism was the institutional separation of church and state and the recognition of liberty, especially religious liberty, as an inalienable right.
Viewed in historical context, the logical connection between religious heresy and political liberty becomes evident. Church and state were once one in Western Civilization. Protestantism itself was a "dissident" movement and as such, dissident Protestants were subject to terrible mistreatment by the Roman Catholic Church or other dominant Protestant sects. And it was through this experience of mistreatment that dissident Protestants first began to argue for religious and political liberty. The theological unitarians, because they believed in what the orthodox considered soul damning heresies, were the most dissident of the dissidents. Think of John Calvin having Michael Servetus burned at the stake simply for publicly denying the Trinity!
As such unitarian theologians who risked death by publicly proclaiming their secret religious convictions had compelling reasons to argue for the separation of church and state and the establishment of religious and political liberty.
In any event, I hope this serves as a partial answer as to why I think studying religious disputes, heresies, Trinity denial, etc. is relevant to the history of America and American liberty.